相关论文: Faster and more accurate computation of the $\math…
In this paper, an $\mathscr{H}_2$ norm-based model reduction method for linear quantum systems is presented, which can obtain a physically realizable model with a reduced order for closely approximating the original system. The model…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
We consider the problem of locating a nearest descriptor system of prescribed reduced order to a descriptor system with large order with respect to the ${\mathcal L}_\infty$ norm. Widely employed approaches such as the balanced truncation…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Over the past few years, Batch-Normalization has been commonly used in deep networks, allowing faster training and high performance for a wide variety of applications. However, the reasons behind its merits remained unanswered, with several…
We deal with the problem of numerically computing the dual norm, which is important to study sparsity-inducing regularizations (Jenatton et al. 2011,Bach et al. 2012). The dual norms find application in optimization and statistical…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…
The need to compute small con-eigenvalues and the associated con-eigenvectors of positive-definite Cauchy matrices naturally arises when constructing rational approximations with a (near) optimally small $L^{\infty}$ error. Specifically,…
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…
In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…
We provide faster algorithms for approximately solving $\ell_{\infty}$ regression, a fundamental problem prevalent in both combinatorial and continuous optimization. In particular, we provide accelerated coordinate descent methods capable…
This paper examines the $\mathcal{H}_\infty$ performance problem of the edge agreement protocol for networks of agents operating on independent time scales, connected by weighted edges, and corrupted by exogenous disturbances.…
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…
We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and H\"older continuous Hessians. The proposed algorithm is a heavy-ball method equipped with two particular restart mechanisms. It…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
The problem of estimating the $\mathcal{H}_\infty$-norm of an LTI system from noisy input/output measurements has attracted recent attention as an alternative to parameter identification for bounding unmodeled dynamics in robust control. In…
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix…
An eigenvalue based framework is developed for the H-infinity norm analysis and its norm minimization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations (DDAEs). For these equations…